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CSC 533: Programming Languages Spring 2012

CSC 533: Programming Languages Spring 2012. Functional programming LISP & Scheme S-expressions: atoms, lists functional expressions, evaluation, define primitive functions: arithmetic, predicate, symbolic, equality, higher-order special forms: if, cond recursion: tail vs. full.

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CSC 533: Programming Languages Spring 2012

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  1. CSC 533: Programming LanguagesSpring 2012 • Functional programming • LISP & Scheme • S-expressions: atoms, lists • functional expressions, evaluation, define • primitive functions: arithmetic, predicate, symbolic, equality, higher-order • special forms: if, cond • recursion: tail vs. full

  2. Functional programming • imperative languages are modeled on the von Neumann architecture • in mid 50's, AI researchers (Newell, Shaw & Simon) noted that could define a language closer to human reasoning • symbolic • (dynamic) list-oriented • transparent memory management in late 50's, McCarthy developed LISP (List Processing Language) • instantly popular as the language for AI • separation from the underlying architecture tended to make it less efficient (and usually interpreted)

  3. LISP • LISP is very simple and orthogonal • only 2 kinds of data objects • atoms (identifiers, strings, numbers, …) • lists (of atoms and sublists) unlike arrays, lists do not have to store items of same type/size do not have to be stored contiguously do not have to provide random access • all computation is performed by applying functions to arguments in pure LISP: no variables, no assignments, no iteration • functions and function calls are also represented as lists no distinction between program and data

  4. Scheme • Scheme was developed at MIT in the mid 70's • clean, simple subset of LISP • static scoping • first-class functions • efficient tail-recursion function calls appear as lists:(FUNC ARG1 ARG2 … ARGn) • (+ 3 2) 5 • (+ 3 (* 2 5)) 13 • (car '(foo bar biz baz)) foo • (cdr '(foo bar biz baz)) (bar biz baz) quote symbol denotes data - not evaluated by the interpreter - numbers are implicitly quoted car : returns first element of list cdr : returns rest of list

  5. Scheme functions • Scheme functions are also defined as lists (MORE DETAILS LATER) (define (FUNC ARG1 ARG2 . . . ARGn) RETURN_EXPRESSION) (define (square x) (define (last arblist) (* x x)) (car (reverse arblist))) • (square 3)  (last '(a b c)) 9 c • (square 1.5)  (last '(foo)) 2.25 foo

  6. Obtaining a Scheme interpreter • many free Scheme interpreters/environments exist • Dr. Scheme is an development environment developed at Rice University • contains an integrated editor, syntax checker, debugger, interpreter • Windows, Mac, and UNIX versions exist • can download a personal copy from • http://download.plt-scheme.org/drscheme/ • ignore Racket propaganda, select older 4.2.4 version (4.2.5 crashes for me) • be sure to set Language to "Pretty Big“ • PLAY TIME! Details to follow…

  7. S-expressions • in LISP/Scheme, data & programs are all of the same form: • S-expressions (short for Symbolic-expressions) • an S-expression is either an atom or a list atoms • numbers4 3.14 1/2 #xA2 #b1001 • characters#\a #\Q #\space #\tab • strings"foo" "Dave Reed" "@%!?#" • Booleans#t #f • symbolsDave num123 miles->km !_^_! symbols are sequences of letters, digits, and "extended alphabetic characters" + - . * / < > = ! ? : $ % + & ~ ^ can't start with a digit, case insensitive by default (but can set preferences in Dr. Scheme)

  8. S-expressions (cont.) • lists () is a list (L1 L2 . . . Ln) is a list, where each Li is either an atom or a list for example: • () (a) • (a b c d) ((a b) c (d e)) • (((((a))))) note the recursive definition of a list – GET USED TO IT! also, get used to parentheses (LISP = Lots of Inane, Silly Parentheses)

  9. Functional expressions • computation in a functional language is via function calls (FUNC ARG1 ARG2 . . . ARGn) (car '(a b c)) (+ 3 (* 4 2)) note: functional expressions are S-expressions evaluating a functional expression: • function/operator name & arguments are evaluated in unspecified order note: if argument is a functional expression, evaluate recursively • the resulting function is applied to the resulting values (car '(a b c)) so, primitive car function is called with argument (a b c) evaluates to list (a b c) : ' terminates recursive evaluation evaluates to primitive function

  10. Arithmetic primitives • predefined functions: + - * / • quotient remainder modulo • max min abs gcd lcm • floor ceiling truncate round • = < > <= >= • many of these take a variable number of inputs (+ 3 6 8 4)  21 (max 3 6 8 4)  8 (= 1 (-3 2) (* 1 1))  #t (< 1 2 3 4)  #t • functions that return a true/false value are called predicate functions zero? positive? negative? odd? even? (odd? 5)  #t (positive? (- 4 5))  #f

  11. Data types in LISP/Scheme • similar to JavaScript, LISP/Scheme is dynamically typed • types are associated with values rather than variables, bound dynamically numbers can be described as a hierarchy of types number complex real MORE GENERAL rational integer integers and rationals are exact values, others can be inexact • arithmetic operators preserve exactness, can explicitly convert (+ 3 1/2)  7/2 (+ 3 0.5)  3.5 (inexact->exact 4.5)  9/2 (exact->inexact 9/2)  4.5

  12. Symbolic primitives • predefined functions: car cdr cons • list list-ref length member • reverse append • (list 'a 'b 'c)  (a b c) • (list-ref '(a b c) 1)  b • (member 'b '(a b c))  (b c) • (member 'd '(a b c))  #f • car and cdr can be combined for brevity (cadr '(a b c))  (car (cdr '(a b c)))  b cadr returns 2nd item in list caddr returns 3rd item in list cadddr returns 4th item in list (can only go 4 levels deep)

  13. Equality primitives equal? compares 2 inputs, returns #t if equivalent, else #f • (equal? 'a 'a)  #t • (equal? '(a b) '(a b))  #t • (equal? (cons 'a '(b)) '(a b))  #t other (more restrictive) equivalence functions exist eq?compares 2 symbols (efficient, simply compares pointers) eqv?compares 2 atomics (symbols, numbers, chars, strings, bools) -- less efficient, strings & numbers can't be compared in constant time (eq? 'a 'a)  #t (eqv? 'a 'a)  #t (eq? '(a b) '(a b))  #f (eqv? '(a b) '(a b))  #f (eq? 2 2)  unspecified (eqv? 2 2)  #t equal? uses eqv?, applied recursively to lists

  14. Defining functions • can define a new function using define • a function is a mapping from some number of inputs to a single output (define (NAME IN1 IN2 … INn) OUTPUT_VALUE) (define (square x) (define (next-to-last arblist) (* x x)) (cadr (reverse arblist))) basically, parameter passing is by-value since each argument is evaluated before calling the function – but no copying (instead, structure sharing)

  15. Conditional evaluation • can select alternative expressions to evaluate (if TEST TRUE_EXPRESSION FALSE_EXPRESSION) (define (my-abs num) (if (negative? num) (- 0 num) num)) (define (singleton? arblist) (if (and (list? arblist) (= (length arblist) 1)) #t #f)) and, or, not are standard boolean connectives evaluated from left-to-right, short-circuit evaluation

  16. Conditional evaluation (cont.) • predicates exist for selecting various types symbol? char? boolean? string? list? null? number? complex? real? rational? integer? exact? inexact? note:an if-expression is a special form • is not considered a functional expression, doesn’t follow standard evaluation rules (if (list? x) (car x) (list x)) • anything but #f is considered "true" (if (member 'foo '(biz foo foo bar)) 'yes 'no) test expression is evaluated • if value is anything but #f, first expression is evaluated & returned • if value is #f, second expression is evaluated & returned

  17. Multi-way conditional • when there are more than two alternatives, can • nest if-expressions (i.e., cascading if's) • use the cond special form (i.e., a switch) (cond (TEST1 EXPRESSION1) (TEST2 EXPRESSION2) . . . (else EXPRESSIONn)) • (define (compare num1 num2) (define (my-member item lst) • (cond ((= num1 num2) 'equal) (cond ((null? lst) #f) • ((> num1 num2) 'greater) ((equal? item (car lst)) lst) • (else 'less))) (else (my-member item (cdr lst))))) evaluate tests in order • when reach one that evaluates to "true", evaluate corresponding expression & return

  18. Repetition via recursion • pure LISP/Scheme does not have loops • repetition is performed via recursive functions (define (sum-1-to-N N) (if (< N 1) 0 (+ N (sum-1-to-N (- N 1))))) (define (my-member item lst) (cond ((null? lst) #f) ((equal? item (car lst)) lst) (else (my-member item (cdr lst))))) (define (my-length lst) IN-CLASS EXERCISE )

  19. Tail-recursion vs. full-recursion • a tail-recursive function is one in which the recursive call occurs last (define (my-member item lst) (cond ((null? lst) #f) ((equal? item (car lst)) lst) (else (my-member item (cdr lst))))) • a full-recursive function is one in which further evaluation is required (define (sum-1-to-N N) (if (< N 1) 0 (+ N (sum-1-to-N (- N 1))))) each full-recursive call requires a new activation record on the run-time stack with tail-recursion, don't need to retain current activation record when make call • can discard the current activation record, push record for new recursive call • thus, no limit on recursion depth (each recursive call reuses the same memory) • Scheme interpreters are required to perform this tail-recursion optimization

  20. Tail-recursion vs. full-recursion (cont.) • any full-recursive function can be rewritten using tail-recursion • often accomplished using a help function with an accumulator (define (factorial N) (if (zero? N) 1 (* N (factorial (- N 1))))) (define (factorial N) (factorial-help N 1)) (define (factorial-help N value-so-far) (if (zero? N) value-so-far (factorial-help (- N 1) (* N value-so-far))))) value is computed "on the way up" (factorial 2)  (* 2 (factorial 1))  (* 1 (factorial 0))  1 value is computed "on the way down" (factorial-help 2 1)  (factorial-help 1 (* 2 1))  (factorial-help 0 (* 1 2))  2

  21. Scoping in Scheme • unlike early LISPs, Scheme is statically scoped • can nest functions and hide details (define (factorial N) (define (factorial-help N value-so-far) (if (zero? N) value-so-far (factorial-help (- N 1) (* N value-so-far)))) (factorial-help N 1)) • since factorial-help is defined inside of factorial, hidden to outside • since statically scoped, arguments in enclosing function are visible to enclosed functions (i.e., non-local variables)

  22. When tail-recursion? (define (sum-1-to-N N) (define (sum-help N sum-so-far) (if (< N 1) sum-so-far (sum-help (- N 1) (+ N sum-so-far)))) (sum-help N 0)) (define (my-length lst) IN-CLASS EXERCISE (length-help lst 0)) usually, a full-recursive solution is simpler, more natural • for a small number of repetitions, full-recursion is sufficient • for a potentially large number of repetitions, need tail-recursion

  23. Higher-order primitives • (apply FUNCTION LIST)applies the function with the list elements as inputs (apply + '(1 2 3))(+ 1 2 3) 6 (apply min '(5 2 8 6))(min 5 2 8 6) 2 • (map FUNCTION LIST)applies the function to each list element (map sqrt '(9 25 81))(list (sqrt 9) (sqrt 25) (sqrt 81)) (3 5 9) (map car '((a b) (c d) (e))) (list (car '(a b)) (car '(c d)) (car '(e))) (a c e)

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